Title:Deformation cohomology for cyclic groups acting on polynomial rings
Abstract:
Hochschild cohomology records information about the deformations of an algebra. Many algebras of interest arise as deformations of skew group algebras, such as graded Hecke algebras, symplectic reflections algebras, and rational Cherednik algebras. We give an explicit description of the Hochschild cohomology governing graded deformations of skew group algebras for cyclic groups acting on polynomial rings. A description of this cohomology is known in the nonmodular setting (i.e., when the characteristic of the field and the order of the group are coprime), but much less is known in the modular setting (i.e., when the characteristic of the field divides the order of the group).